Dynamic modelling of the physiology of breathing to improve mechanical ventilation

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Dynamic modelling of the physiology of breathing to improve mechanical ventilation

MASTER THESIS

J. I. de Jong s1727583

Faculty of Science and Technology Biomedical Signals and Systems EXAMINATION COMMITTEE Prof.dr. L.M.A. Heunks A. Jonkman, MSc.

Dr. E. Mos – Oppersma Prof.dr.ir. P.H. Veltink

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Dynamic modelling of the physiology of breathing to improve mechanical ventilation

Date of publication: 05-07-2021 Author: J.I. de Jong

Student number: s1727583

Field of education: biomedical engineering

Examination committee: Prof.dr. L.M.A. Heunks, Drs. A. Jonkman, Dr. E. Mos – Oppersma, Prof.dr.ir. P.H.

Veltink

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Summary

Mechanical ventilation is the mainstay of supportive therapy in the intensive care unit for patients with respiratory failure. Although life-saving, mechanical ventilation may also cause secondary lung injury. Settings poorly adapted to the patient’s physiology may result in poor outcome; however, finding the optimal settings for the individual patient is still an ongoing debate. As a result, the ventilation may not always be optimally adapted to the individual patient which may have negative effects on the patient’s lungs and respiratory muscle function and may worsen clinical outcomes, including the increase of the duration of ventilation.

Our hypothesis was that a closed-loop mechanical ventilation system that is based on a model that considers a limited set of well-chosen aspects of the physiology of breathing may be able to improve these limitations. The aim of this thesis was to develop a simple but credible model that is aimed towards this objective. This model may be the initial step towards incorporating such a system in clinical practice and may provide a first insight in the clinical applicability in the context of the critically ill mechanically ventilated patient.

From the literature review and conversations with clinicians it resulted that a model of the gas exchange and the respiratory drive with low complexity could be of an improvement to current clinical practice by increasing the insight in the patient’s respiratory parameters and variables and predicting patient responses to changes in ventilator settings.

A two-compartment model based on the gas exchange was developed of which the dynamical behaviour consists of a slow and a fast exponential component. The model reaches an

equilibrium state that is dependent on the minute ventilation. For carbon dioxide, this behaviour complies with the behaviour found in an experimental study that was conducted in a healthy volunteer. Aggregated model parameter groups could be identified, and predictions could be made with the identified model that were qualitatively similar to the results of the experimental study. While the limited observability and resources limit the possibilities for extensive model validation, this gives an indication that the simple model may have the right structure to describe the gas exchange of carbon dioxide.

The developed model may be an addition to current clinical practice by improving the clinician’s insight into the efficiency of the gas exchange of patients on mechanical ventilation. This may give the clinician an improved insight into the readiness of the patient for weaning and may make better-substantiated ventilator setting choices possible. Increased testing and

experimental validation are required before clinical application is possible.

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Glossary

name definition

accessory muscles The muscles that assist in breathing but do not play a primary role.

acute respiratory distress

syndrome A type of respiratory failure characterized by rapid onset of widespread inflammation in the lungs.

airway occlusion pressure The pressure generated at the airways during a period of no airflow in the airways.

alveolar dead space The sum of the volumes of the alveoli which have little or no blood flowing through their capillaries.

alveolar infiltration A substance denser than air, e.g. blood or pus, which lingers within the lungs.

assisted ventilation Mode of ventilation where the inspiratory efforts of the patient are detected and ventilatory assist is delivered accordingly.

blood gasses Measurement of the concentration of pH, oxygen, carbon dioxide and several other components present in a sample of blood.

breathing effort The energy-consuming activity of the respiratory muscles aimed at driving respiration.

controlled ventilation A mode of ventilation in which the ventilator delivers the pre-set volume or pressure regardless of the patient's own inspiratory efforts.

dynamical analysis An area of mathematics used to describe the behaviour of complex dynamical systems, usually through differential equations.

eigenvalue A scalar that describes the relationship between the individual system state variables and their derivatives.

equilibrium state The state of a system in which properties have constant values if external conditions are unchanged.

order of system The number of independent energy storage elements in the system.

parameter identification The determination of the most optimal combination of values of the model parameters.

patient-ventilator asynchrony A mismatch between the patient’s respiratory system and the ventilator, regarding time, flow, volume, or pressure demands.

PEEP The pressure in the lungs above atmospheric pressure at the end of expiration.

pulmonary fibrosis A lung disease that occurs when lung tissue becomes scarred and damaged.

pulmonary shunt The passage of venous blood through the lungs without participation in gas exchange.

respiratory mechanics The mechanical properties of the pulmonary system; the airway pressures, airflow rate and lung volumes.

spontaneous breathing trial A trial that assesses the patient's ability to breathe while receiving minimal or no ventilatory support.

time constant the duration in seconds during which a variable rises of falls exponentially and becomes 63.2% of its final value.

observability A measure of how well internal states of a system can be retrieved from measured outputs.

ventilation-perfusion

mismatch A condition in which one or more areas of the lung receive either no oxygenated air or no blood flow.

ventilator-induced lung injury An acute lung injury that develops during mechanical ventilation.

weaning The process of reducing ventilatory support, ultimately resulting in a patient breathing spontaneously and being disconnected from the ventilator.

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1. Introduction

1.1. Background and research problem

It is probable that somewhere in the next decade patients and clinicians will arrive at the hospital in self-driving cars. This makes it hard to imagine that mechanical ventilation, which is the mainstay of supportive therapy in the intensive care unit for patients with respiratory failure, is still mainly manually operated. This clinician-in-the-loop system is labour-intensive and requires expert knowledge [1]. Settings poorly adapted to the patient’s physiology may result in poor outcome; however, finding the optimal settings for the individual patient is still an ongoing debate. As a result, mechanical ventilation may not always be optimally adapted to the individual patient which may have negative effects on the patient’s lungs and respiratory muscle function and may worsen clinical outcomes, including the increase of the duration of ventilation.

Closed-loop mechanical ventilation systems have been the subject of research for a long time.

Closed-loop mechanical ventilation is in essence the automatic control of ventilator settings based on measured physiological variables. In figure 1 the workflow of simple closed-loop mechanical ventilation is presented schematically. In this example, the system has one

physiological variable that is controlled. The clinician sets a desired value for this variable, and the variable is constantly measured with a sensor and compared to the desired value. The controller will determine the difference between the actual value and the desired value and give an appropriate adjustment of ventilator settings. This adjustment in ventilator settings should impose changes in patient ventilation that should bring the controlled physiological variable to the desired value. Since these desired values or target ranges of physiological variables depend on the initial parameters set by the clinician, it is of utmost important that these are

programmed correctly for the individual patient.

Figure 1 Schematic overview of closed-loop mechanical ventilation.

Closed-loop mechanical ventilation systems that involve the measurement of multiple variables to control multiple settings are able to mimic the response of real human physiology closely [2].

The controllers of these advanced closed-loop mechanical ventilation systems are often based on models that aim to describe the state of the patient being controlled.

In the recent years, several advanced closed-loop mechanical ventilation systems have been developed. An example is the automated system INTELLiVENT-adaptive support ventilation (ASV) [3, 4]. This system controls the respiratory rate, tidal volume, end-tidal carbon dioxide and oxygen saturation by automatic adaption of the ventilator settings. A limitation of automated modes, such as ASV, is that the patient’s breathing effort is not measured directly.

Proportional closed-loop mechanical ventilation systems do consider patient effort and adjust ventilatory support proportional to this effort. An example of a proportional system is neurally adjusted ventilatory assist (NAVA) that measures the electrical activity of the diaphragm (EAdi) via electrodes embedded on a nasogastric catheter to control the ventilator output [5].

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Although the current closed-loop mechanical ventilation systems seem promising, there is room for further improvement. The closed-loop mechanical ventilation systems that are used in current practice mainly focus on the mechanics of breathing. For example, there are currently no commercially available closed-loop systems that consider the metabolism, efficiency of the gas exchange and the acid-base balance [6]. As a result, the clinician must set most of the ventilator settings manually. Choosing the optimal ventilator settings may be challenging because insight in certain parts of the physiological state of the patient may be low. Throughout the duration of mechanical ventilation, it is therefore often unknown what the optimal combination of ventilator settings is for the individual patient [1]. As a result, the ventilation may not be optimally adapted to the individual patient throughout the duration of mechanical ventilation. A stated before, this may have negative effects on the patient’s lungs and respiratory muscle function and may worsen clinical outcomes, including the increase of the duration of ventilation.

Our hypothesis is that a closed-loop mechanical ventilation system that is based on a model that considers a limited set of well-chosen aspects of the physiology of breathing to determine the optimal ventilator settings may be able to improve these limitations. The physiological model, that forms the basis of the system, could provide insight in patient specific respiratory

parameters and variables that cannot be directly obtained from current routine clinical measurements. This would provide constant insight into a patient’s physiological state which may enable individualization and optimization of patient treatment [7, 8]. This may limit the negative consequences of mechanical ventilation on the patient's breathing function, and hence, it may reduce the time spent on mechanical ventilation, which is clinically and economically important [6, 9, 10].

1.2. Research questions

The aim of this thesis is to develop a simple but credible model of the physiology of breathing based on the difficulties encountered in current clinical practice. This model will be the initial step towards the use of a closed-loop system based on a model of the full physiology of breathing in clinical practice and will allow for a first insight in the clinical applicability.

The research questions of this thesis are:

- What is the state-of-the-art of closed-loop mechanical ventilation?

- How can model-based closed-loop mechanical ventilation be used to improve the current clinical practice of mechanical ventilation?

- What dynamic model of the physiology of breathing satisfies these requirements?

- What is the dynamic behaviour of the developed model?

- What relevant information about the dynamic behaviour of the real breathing system can be obtained from experimental measurements?

- How can this information be used to evaluate the model’s ability to identify the respiratory parameters and predict the ventilatory responses?

1.3. Approach and outline of this thesis

To answer these questions, several actions were performed. First, a literature review of the current state-of-the-start was conducted. Parallel to this literature review, conversations with clinicians and a literature research were conducted to specify the possible improvements that a model of the physiology of breathing could add to current clinical practice. Subsequently, a model was developed aiming to satisfy these requirements. A dynamical analysis of the model

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used to assess the validity of the model structure and the identifiability of the respiratory parameters.

The overall structure of this thesis takes the form of six chapters. Chapter 2 begins by describing the state-of-the art and the possible improvements that can be achieved in current clinical practice by using model-based closed-loop mechanical ventilation. Chapter 3 describes the development and the dynamical analysis of the model. Chapter 4 describes the design of the experiment and the obtained experimental results. Chapter 5 contains a discussion about the implications and limitations of the presented concepts and results and suggestions for further research. The thesis finishes with a conclusion in chapter 6.

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2. State-of-the-art of closed-loop mechanical ventilation and possible improvements.

Before the development of the model can start, it is crucial to determine what the desirable improvements in current clinical practice are. Subsequently, it can be determined what components and functions the model should encompass. To create a complete overview, the general workflow of mechanical ventilation is discussed briefly in section 2.1. In section 2.2. it is described what the current state-of-the-art of closed-loop mechanical ventilation is. In section 2.3. the possible improvements that can be obtained in clinical practice using a new model- based closed-loop mechanical ventilation system are described. In section 2.4. the most

important results are summarized, interpreted and their implications for the development of the model are stated.

2.1 General overview of the workflow mechanical ventilation

The duration of mechanical ventilation can be roughly and globally divided into three global stages, but this may vary between patients according to the indication for mechanical ventilation. Each stage has different aims and conditions regarding to the monitoring of parameters and variables.

The first stage starts when a patient arrives at the ICU with respiratory failure and/or an

indication to intubate and start mechanical ventilation. The patient is often sedated and is put on controlled mechanical ventilation. During controlled mechanical ventilation, the patient cannot breathe spontaneously. The main aim of this stage is to give the lungs time to repair. It is therefore very important to monitor the pressures and the volumes applied to the lungs which should stay low to prevent further injury and inflammation (e.g., ventilator-induced lung injury).

The blood gases should stay between predetermined safe bounds. However, reaching optimal blood gasses comes second to the protection of the lungs. The clinician may for example allow permissive hypercapnia, where a very high carbon dioxide fraction in the blood is allowed for the sake of keeping the tidal volume and pressure low. It is assessed at least daily whether a patient on a controlled mode of ventilation can be switched to an assisted form of ventilation and sedation can be lowered.

When the lungs have mostly healed, the next stage of mechanical ventilation starts. The aim of this stage is to recover the breathing function of the patient. In this stage, the patient is on assisted ventilation, during which the ventilator detects inspiratory effort of the patient and delivers pressure assist accordingly. During this stage, the lungs can handle a larger range of pressures and volumes. As a result, the clinician can choose higher values for the applied tidal volume which may make it easier to reach the desired blood gasses. It is assessed regularly whether the level of ventilatory support can be reduced.

The last stage is the weaning stage and starts when the patient is still on the ventilator but seems to be able to breathe sufficiently with low support (PEEP <8, FiO2<0.5). Weaning is the term used to describe the process of withdrawing the ventilatory support and eventually removing the patient from the ventilator. It is not always clear when a patient is ready for weaning. As a result, the clinician needs to trust in his own insight and experience. The patient will start a spontaneous breathing trial (SBT), during which the patient is not yet extubated but does not receive any support or a limited amount of ventilator support, allowing to test the readiness for weaning of the ventilator. Throughout the SBT, which usually takes 30 minutes, respiratory parameters and blood gases are monitored. If sufficient, the patient can be released

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hand, there are indications that weaning sometimes takes place later than strictly necessary [31].

The current closed-loop mechanical ventilation systems often only focus on one stage of mechanical ventilation. For example, there are several closed-loop systems that solely focus on the breathing mechanics and are only usable during the first stage. In the next section, the closed loop mechanical ventilation systems that are used in current clinical practice are described.

2.2. The state-of-the-art of closed-loop mechanical ventilation.

In this section, several examples of closed loop mechanical ventilation systems are given. The systems are categorized based on the controlled physiological variable or variables.

Closed-loop control based on gas exchange

Several closed loop models based on the control of oxygen have been developed. Most of these systems are focussed on neonates. The AVEA-CLiO2 is a commercially available system for neonates based on oxygenation control [11]. This system controls the oxygen saturation and maintains this variable within a target range by adapting the fraction of inspired oxygen. A study of Salverda et al. (2021) that included a total of 588 infants found that the use of the system did not lower the mortality or morbidity, but did reduce the duration of invasive ventilation [12].

No commercial systems that are solely based on the control of carbon dioxide have been developed thus far. In a study of Martinoni et al. (2004) a model-based control system was created that controls the end-tidal carbon dioxide fraction by adjusting the minute ventilation.

The system is based on a model of Chiari et al. that consists of three compartments: lung, brain and body tissue [13]. The system was tested in clinical settings and the model-based controller seemed to meet the requirements for routine clinical application [14]. However, clinical implementation has never been achieved.

The former systems were based on either the control of carbon dioxide or oxygen. A recently developed system of Hermand et al. (2016) controls both the partial pressures of oxygen and carbon dioxide in the arterial blood. A mathematical model that mimics the central and

peripheral chemoreceptor responses in humans uses the values of the partial pressures to adjust the minute ventilation. The model response matches with experimental data but the model has not been tested in clinical practice thus far [15].

A disadvantage of the closed-loop ventilation strategies presented in the former section, is that they focus only on the gas exchange and do not consider the lung mechanics. Achieving proper oxygenation and emission of carbon dioxide may require large tidal volumes or ventilator pressures, which may cause ventilator-induced lung injury (VILI). With clinical ventilation strategies becoming focused on protective ventilation that aims to prevent VILI, the lung mechanics are an important aspect to take into consideration [6].

Closed-loop control based on the respiratory mechanics

Most closed-loop mechanical ventilation systems used in current clinical practice are mainly based on the respiratory mechanics. An example is adaptive support ventilation (ASV) that controls the minute ventilation by finding the optimum combination of respiratory rate and tidal volume based on the respiratory mechanics of the patient. The respiratory mechanics consist of the lung compliance, airway resistance and expiratory time constant [4]. This principle is based on the Otis equation which states that there is an optimum respiratory rate that minimises the breathing effort [16].

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Another example is SmartCare that adapts the delivered pressure support level to the patient’s effort. The system continuously determines the patient’s respiratory mechanics and patterns.

The aim is to simulate clinical reasoning to avoid under- or over-assistance during mechanical ventilation by constantly adjusting the level of pressure support. These frequent adjustments in pressure support would be unrealistic if attempted by a clinician. The system also has an automated weaning protocol that consists of an automated reduction of pressure support level and thereafter an automated spontaneous breathing test.[17]

Closed-loop control based on the multiple components of the physiology

Recently, researchers and industry have presented automated systems which are based on a culmination of the categories described before. This encompasses maintaining optimal blood gasses, preventing VILI and improving patient-ventilator synchrony.

INTELLiVENT-ASV is a system based on ASV that provides automatic gradual decreases in inspiratory support levels to facilitate weaning of the patient from the ventilator [22]. This system controls the respiratory rate, tidal volume, end-tidal carbon dioxide and oxygen saturation by automatic adaption of the ventilator settings to reach target values set by the clinician. The ventilator setting that are adapted are the fraction of inspiratory oxygen, minute ventilation and positive end-expiratory pressure. The system has shown to be feasible and able to deliver protective ventilation in passive and spontaneously breathing patients with different lung conditions [23]. However, there are few experienced facilities where INTELLiVENT-ASV can be used, and therefore, its usage status and efficacy have not yet been reported [24]. One of the reasons for this is that the clinical situations in which INTELLiVENT-ASV should be used have not yet been clarified.

Other systems are developed but not yet commercialized. An example is the system of Schwaiberger et al. (2018). This system reacts protocol-driven to any measured change in respiratory mechanics or oxygenation. It controls the airway pressures, oxygen saturation and end-tidal carbon dioxide fraction by adjusting the tidal volume, PEEP, respiratory rate and the fraction of inspired oxygen accordingly. A pilot animal study showed promising results, but clinical trials have yet to be performed [25].

Closed-loop control based on breathing effort

The former described automated modes integrate closed-loop principles but do not directly measure patient effort. Proportional modes of ventilation are assisted modes of ventilation that measure patient effort and deliver assistance proportional to this effort [18].

Proportional assist ventilation with load-adjustable gain factors (PAV+) determines the inspiratory effort of the patient by measuring the volume and airflow being pulled in by the patient. End-inspiratory occlusions are used to determine the respiratory system resistance (𝑅_!") and elastance (𝐸_!") every couple of breaths. 𝑅_!" is the resistance of the respiratory tract to airflow and 𝐸_!" is the measure of the elastic properties of the lung and pleura. Using equation 1, the ventilator can calculate the total pressure that is delivered to the respiratory system (𝑃_!"!#$ ).

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𝑃_!"!#$ = 𝑃_%&'! + 𝑃_()*+$& = (𝑎𝑖𝑟𝑓𝑙𝑜𝑤 × 𝑅_𝑟𝑠) + (𝑣𝑜𝑙𝑢𝑚𝑒 × 𝐸_𝑟𝑠) (1)

PAV+ is designed in a way that the work is shared between the patient and the ventilator. The

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70 percent, the ventilator will provide 70 percent of the calculated total pressure, the remaining being assumed by the patient’s respiratory muscles [19].

Neurally adjusted ventilatory assist (NAVA) is an assisted ventilation mode that measures the electrical activity of the diaphragm (EAdi) via transoesophageal electromyography using a modified nasogastric catheter with electrodes at the level of the diaphragm [5]. The EAdi is used to control the ventilator: ventilator assist is provided proportional to the EAdi over the full inspiratory phase according to a gain (NAVA level, in cmH2O/uV) set by the clinician. Improved patient-ventilator synchrony for this system was shown by Piquilloud et al. [20]. Vahedi et al.

showed positive staff experiences with the use of NAVA in clinical practice [21]. One drawback is that NAVA is only available on one ventilator brand, which hinders widespread implementation.

NAVA can be used with both noninvasive and invasive mechanical ventilation. In addition, EAdi monitoring is available in other modes than NAVA as well, as a measure to monitor diaphragm activity and patient-ventilator interaction in order to further optimize ventilation management.

Model-based decision support systems

Systems have been created that computerize clinical protocols which medical staff use to adapt mechanical ventilator settings. These decision support systems are not able to make changes to the ventilator themselves but propose the changes to the clinician. Even though these systems are not closed-loop systems, they are described in this section because of their similarities with closed loop systems.

The INVENT system, recently commercialised as the Beacon Caresystem, is an open-loop system that combines a set of physiological models describing pulmonary gas exchange, lung mechanics, ventilation, the acid-base chemistry of blood, respiratory drive and metabolism [9, 26]. The Beacon Caresystem presents advice for ventilator adjustments and the physiological rationale behind this advice. A study by Spadaro et al. (2018) has shown that use of the Beacon

Caresystem resulted in appropriate responses to changes in pressure support levels while acting to preserve respiratory muscle function [27, 28]. It is currently being researched if the use of the decision support system over the entire duration of ICU stay will reduce the time spent on mechanical ventilation and the difficulty of the weaning process [26].

Another decision support model that is currently being developed is the Lung and Diaphragm Protective Ventilation (LDPV) model, aiming to assist the clinician in adjusting mechanical ventilation settings toward target ranges that are considered safe for the lungs and the

diaphragm. The model considers the respiratory drive, pharmacokinetics of propofol, acid–base homeostasis, ventilator settings and lung and respiratory muscle mechanics. It differs from existing mechanical ventilation models by focusing on output indicators that reflect lung and diaphragm safety. This model has not been tested in clinical settings, but initial simulations have produced results which demonstrate simulated physiological responses consistent with what is expected.[7]

Overview

In table 1 an overview is given of the closed loop systems described in this section. The model- based decision support systems are not included.

Table 1 Overview of the state-of-the-art systems described in this section.

system controlled variable adapted variable source

Martinoni et al.

(2004) End-tidal 𝐶𝑂# Minute ventilation [14]

Hermand et al. Partial pressure arterial 𝐶𝑂# and 𝑂# Minute ventilation [15]

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AVEA-CLiO2 𝑂_# saturation fraction of inspired 𝑂_# [11]

ASV Breathing effort Tidal volume, respiratory rate [4]

Dräger SmartCare Respiratory rate, tidal volume, end-tidal 𝐶𝑂_# Pressure support level [23]

PAV+ Airflow, volume Pressure support level [4]

NAVA Electrical activity of the diaphragm Triggering, level of inspiratory assist,

cycle-off [5]

INTELLiVENT-ASV Respiratory rate, tidal volume, end-tidal 𝐶𝑂_#,

𝑂_# saturation Respiratory rate, tidal volume,

inspiratory time, PEEP, fraction of inspired 𝑂#

[23]

Schwaiberger et al.

(2018) Airway pressures, tidal volume, end-tidal 𝐶𝑂_#,

𝑂# saturation Tidal volume, PEEP, respiratory rate,

I:E-ratio and fraction of inspired 𝑂# [25]

2.3. Possible improvements of current clinical practice with a model-based closed-loop system

In the introduction the hypothesis was stated that model-based closed-loop mechanical ventilation systems could be of use by providing insight in the important patient’s specific parameters. This would result in ventilator settings that are optimally adapted to the individual patient. To improve the specification of the clinical problem, we have spoken to an intensivist and a technical physician specialized in the respiratory system of the Amsterdam UMC and a respiratory physiologist of the Medisch Spectrum Twente. The questions that were asked during these conversations are presented in appendix 4. We have also searched in literature for the difficulties that are encountered in monitoring the important parameters and choosing the optimal ventilator settings. The possibilities for a system based on a model of the physiology of breathing to overcome these difficulties are described at the end of this section.

Monitoring the mechanical properties of the respiratory system

Accurate monitoring of the mechanical properties of the respiratory system is important to understand respiratory failure in patients on mechanical ventilation and to optimize mechanical ventilation settings [32]. There are several parameters that describe the mechanical properties of the respiratory system. The first is the respiratory system compliance which is the measure of the lung and chest wall’s ability to stretch and expand. The compliance can be determined from the tidal volume (V_!), the plateau pressure (𝑃_,$#!) and total positive end-expiratory pressure (PEEP).

𝐶_-* = V_!

𝑃_./01− 𝑃𝐸𝐸𝑃_!"! (2)

The respiratory resistance is the resistance of the respiratory tract to airflow during inhalation and exhalation. Airway resistance can be measured by dividing the difference between the plateau pressure (𝑃_./01) and the peak pressure (𝑃_.203) by the airflow in liters per second (𝜙_#4-).

𝑅_-* =𝑃_.203− 𝑃_./01

𝜙_#4- (3)

During controlled modes of ventilation, a simple end-inspiratory occlusion maneuver is used to compute 𝑃 and 𝑃 , whereas an end-expiratory occlusion is performed for measurement

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During assisted ventilation, obtaining an inspiratory hold and measurement of pulmonary mechanics may be complicated because of the combination of both ventilator and respiratory muscle pressures during inspiration [32]. It may then be necessary to use an esophageal balloon catheter for dynamic rather than static measures of lung and chest wall mechanics. However, esophageal manometry is minimally invasive and may be complicated to perform [29].

Although several experts have confirmed that the measurement of 𝐶_-* and 𝑅_-* in spontaneously breathing patients is feasible and reliable, it is still rarely applied in the clinical practice [32, 33].

In addition, not all available mechanical ventilation systems allow occlusion maneuvers during assisted ventilation modes [29].

Monitoring the gas Exchange

The gas exchange describes the movement of oxygen and carbon dioxide between the alveoli and the capillaries in the lungs. An impaired gas exchange may have several causes, e.g.

pulmonary shunt, ventilation-perfusion (V/Q) mismatch and alveolar dead space [34]. In clinical practice, description of the efficiency of the gas exchange is limited to two single lumped indices [9]. For oxygen, this is the ratio between the partial pressure of oxygen in the arterial blood and the fraction of inspired oxygen (𝑃_#𝑂₅/𝐹𝑖𝑂₅) which primarily describes oxygenation

abnormalities due to regions of the lung with pulmonary shunt and low V/Q ratio. For carbon dioxide, this is the ratio between the end-tidal carbon dioxide fraction and the partial pressure of carbon dioxide in the arterial blood ( 𝐸𝑡𝐶𝑂₅/𝑃_#𝐶𝑂₅). It is used to approximate the effects of high V/Q ratio and alveolar dead space on 𝐶𝑂₅-elimination [9].

These indices do not allow for separation of the causes of impaired gas exchange. There are indications that in patients with acute respiratory distress syndrome (ARDS), dead space has prognostic value and can be used to guide ventilator settings. Several studies have demonstrated that elevated dead space in patients with ARDS is associated with an increased risk of mortality [35-37]. However, dead space is seldom calculated in clinical practice because it requires the alveolar carbon dioxide fraction, which is difficult to measure or estimate [38].

Monitoring the breathing effort

Breathing effort is the energy-consuming activity of the respiratory muscles aimed at driving respiration. Maintaining patient breathing effort during mechanical ventilation has advantages and disadvantages. The positive effects of maintaining breathing effort are protection against respiratory muscle atrophy and improved oxygenation [39]. The potential negative effect of maintaining breathing effort is patient self-inflicted lung injury where intense effort may generate too large pressures that may be damaging to the lungs [40]. Finding the balance between the former named advantages and disadvantages remains a challenge in mechanical ventilation [41], especially in patients with excessive respiratory drive.

There is no specific diagnostic technique for the assessment of breathing effort. Physicians perform physical examination to assess breathing effort in clinical practice, like recruitment of accessory muscles or an increased respiratory frequency [42]. However, this does not allow for quantitative assessment of breathing effort.

For quantitative assessment of the breathing effort, the parameters work of breathing (WOB) and pressure-time product (PTP) are considered the gold standard. [42]. The WOB is the energy consumed for respiration, often expressed in joule per litre. The PTP is the integral of all

pressures generated by the breathing muscles measured for one minute. For assessment of the WOB and PTP, it is necessary to perform pressure measurements which are difficult to interpret

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and obtain. For this reason, quantitative assessment of the breathing effort is rarely performed in clinical practice and is limited to specialised research facilities [43].

Monitoring the respiratory drive

The respiratory drive describes the intensity of the output of the respiratory centers [44]. There is no technique that can measure the respiratory drive directly. As a result, the respiratory output is used to quantify the respiratory drive. The respiratory drive is often qualitatively assessed by clinical signs, e.g. dyspnea and the use of accessory respiratory muscles. Other examples of assessment are the electrical activity of the diaphragm (EAdi), the airway occlusion pressure and measurement of the esophageal and gastric pressures [44]. Pressure

measurements for inspiratory effort only reflect the respiratory drive if both neural transmission and diaphragm function are functional.

EAdi records the electrical activity of the diaphragm with electrodes incorporated into a

nasogastric tube [45]. This is the output that is closest to the output of the respiratory centers. It is easy the measure, minimally invasive and the activity represents the whole diaphragm. The limitation of EAdi is that there are no normal values because EAdi varies greatly between people.

However, it can be useful to monitor changes in in the diaphragm activity within a patient over time [42].

The airway end-expiratory occlusion pressure is a noninvasive measurement that reflects the output of the respiratory control centre [46]. When an end-expiratory airway occlusion is applied, spontaneous respiratory effort by the patient during the occlusion will generate a negative pressure in the airway pressure that represents the respiratory muscle effort [32].

The esophageal or gastric pressure is measured via an air-filled balloon catheter inserted in the esophagus or stomach [47]. The esophageal pressure (Pes) indicates the level of effort for all inspiratory muscles, while the differential pressure (gastric pressure minus esophageal pressure

= transdiaphragmatic pressure (Pdi)) indicates effort of the diaphragm only. Measurements are rarely done in clinical practice because they are challenging to perform and the results may be difficult to interpret for clinicians[29].

An important limitation of manometry in assessing the respiratory drive is that it is not possible to make a distinction between impairments in the breathing muscles and the neural drive. This imposes the risk of underestimating respiratory drive in patients with respiratory muscle weakness. In these patients, despite a high neural drive (EAdi), inspiratory effort (Pes, Pdi) might be low.

Monitoring the blood gases

Blood gas analysis during mechanical ventilation provides information that allows the assessment of oxygenation, ventilation and acid-base status. Modern blood gas machines measure the partial pressures of oxygen and carbon dioxide and the pH directly. These are then used to calculate the bicarbonate concentration, base excess and oxygen saturation. The blood gasses are measured multiple times per day but there is no standard protocol for the

measurement of the blood gases, which can be a problem in understaffed intensive care units [29].

Possible improvements in monitoring parameters using a model-based closed-loop system

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is the improved identification and observation of the important physiological parameters and variables. A model can provide insight in parameters and variables that cannot be directly obtained from measurements by using measured data to estimate the physiological parameters and variables.

An example of a model that could provide insight in patient specific parameters is the pressure reconstruction model that was developed by Damanhuri et al. (2016). This model was used to calculate how much breathing effort is exerted by the patient during reverse triggering, which is a specific from of patient-ventilator asynchrony in a sedated patient during fully controlled mechanical ventilation. The model’s input were the airway pressures and flow, and no additional clinical protocols or invasive procedures were necessary [48]. It is unlikely that this model can be translated to the spontaneously breathing patient during assisted modes of ventilation, due to differences in airway pressure and flow waveform profiles; however, it would be interesting to further explore whether there are certain airway pressure and flow patterns or parameters that could predict the amount of patient effort in the spontaneously breathing patient.

The identification of parameters through perturbations in the system input may be an important technique to improve insight in the respiratory parameters. Jawde et al. (2020) described a model that can obtain the patient specific respiratory mechanics after application of perturbations in the breathing pattern. The system variates the respiratory rate and tidal volume breath-to-breath. From the measured change in airway pressures and airflows the model can determine the time-dependent respiratory resistance and elastance of the patient [49]. Both models have not yet been tested in clinical practice.

A system that could provide the automatic application of an end-inspiratory and end-expiratory occlusion manoeuvre could provide improved identification of the parameters that describe the respiratory mechanics. From the end-inspiratory occlusion manoeuvre, the respiratory

resistance and compliance can be determined in controlled modes. In assisted modes, the respiratory resistance and compliance could be estimated using short occlusions and models, as is done in PAV+. Through the end-expiratory occlusion the airway occlusion pressure can be obtained which provides insight in the respiratory drive [44].

Measurements that are an addition to those available in routine clinical care may be included to the system to allow for identification of a greater number of parameters [1]. An example is the use of non-invasive sensors. In a study of Doorduin et al. (2016) it was found that the

measurements of end tidal carbon dioxide with volumetric capnography could be used to determine the true Bohr dead space [38].

Continuous transcutaneous measurement of the pH and partial pressures of oxygen and carbon dioxide has been developing for many years, and it may prove useful in capturing respiratory and hemodynamic failures in critically ill patients [50].

Determination of the optimal ventilator settings

Choosing the optimal value for ventilator setting can be challenging because it is not always known what the optimal settings are in certain situations. An example is the pressure support level where there is a trade-off between beneficial and detrimental effects. When ventilating patients with pressure support, the clinical challenge is to determine the level of pressure support which reduces the risk of respiratory muscle atrophy and promotes weaning, without stressing or exhausting the patient and causing diaphragm fatigue, or introducing asynchrony between the patient and the ventilator [9].

Another example is setting the level of positive end-expiratory pressure (PEEP). PEEP has the advantage that is prevents the collapse of the alveoli. However, the disadvantage of PEEP is that

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chosen as low as possible while still preventing alveolar collapse. The optimal level of PEEP is dependent on many factors, e.g. severity of lung damage, degree of recruitability. Studies

comparing low and high PEEP in ARDS patients do not show an unequivocal answer. The choice of PEEP also proves subjective with high inter-clinician variability [51].

The last example given in this section is the level of the fraction of inspired oxygen (𝐹𝑖𝑂₅).

Breathing in air with sufficient oxygen is important to prevent hypoxia. However, there are also dangers to inspiring a high concentration of oxygen for a long duration of time. Examples are the suppression of the respiratory drive, alveolar infiltration and toxicity. Toxicity may cause

inflammation and eventually, pulmonary fibrosis. It is not always possible to determine when the toxic level will be reached and it may therefore be difficult to determine what the optimal value of 𝐹𝑖𝑂₅ is. [52] A high 𝐹𝑖𝑂₅ also causes nitrogen washout. The oxygen molecules will replace the nitrogen molecules in the lungs. When the nitrogen concentrations lower, the alveoli will start to collapse. This may result in hypoxemia because fewer alveoli participate in the gas exchange.

Possible improvements in determination of the optimal ventilator settings using a model-based closed-loop system

In the former paragraphs, it was described that choosing the optimal ventilator settings can be challenging. The optimal ventilator settings often have significant inter-individual variability [1].

The ability of a model-based closed-loop system adapted to the individual patient to predict the response to changing ventilator settings would be a useful addition to clinical practice [53].

Accurate prediction of responses to changing ventilator settings may enable more personalised and efficient ventilation. This will minimise the risk of VILI and may reduce the duration of mechanical ventilation, which is clinically and economically important [10].

Morton et al. (2018) developed and validated a single compartment lung model that uses the information about the lung mechanics available at a low PEEP to predict the lung mechanics at a higher PEEP. The model could accurately predict peak inspiratory pressures after changes in PEEP and could improve clinician confidence in attempting potentially dangerous treatment strategies.[54]

These predictions can be further substantiated with artificial intelligence. With most data becoming digitized, it is plausible that in the future the data that describes the development of the state of the patient will be available to the ventilator [6]. Artificial intelligence may learn about the specific patient response to ventilator changes and can therefore provide predictions.

An example is the artificial neural network model developed by Kuo et al. (2015). This model receives a set of variables belonging to the subjects’ characteristics and the breathing pattern and uses artificial intelligence to determine the chance of successful extubation. In clinical practice, this model could help clinicians to select the appropriate earliest weaning time. The downside of using a predictive model based on artificial intelligence compared to a regular predictive model is that the model is not transparent for clinicians and the reasoning behind decisions is not available [55]. These models are also solely based on routinely obtained 'standard' measurements, and not on in-depth physiology or patient effort.

2.4. Implications of the desirable improvements for the design of the model

The closed-loop mechanical ventilation systems that are used in current clinical practice mainly

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do not consider the different stages of mechanical ventilation described in section 2.1 and are therefore not usable throughout the whole duration of mechanical ventilation.

In section 2.3. it was described that obtaining insight in important parameters that describe the physiological state of the patient is often challenging. During assisted ventilation, it is difficult to obtain insight in the respiratory mechanics, the breathing effort and the respiratory drive because of the combination of ventilator and patient efforts. Other parameters, like the physiological dead space, are useful to acquire but require difficult measurements.

It was also described that selecting ventilator settings can introduce a difficult balance between sufficient oxygenation, prevention of breathing function degeneration and prevention

of ventilator-induced lung injury [56]. Throughout the duration of mechanical ventilation, it is often unknown what the optimal combination of ventilator settings is for the individual patient [1]. The chosen combinations of ventilator settings often vary among clinicians in similar situations [57].

In section 2.3. the possible improvements that a new model-based closed-loop ventilation system could add to current practice were described. The first improvement is the improved identification and observation of the important physiology parameters and variables that cannot be measured directly. A model could provide insight in parameters and variables that cannot be directly obtained from measurements by using measured data to estimate the values. When insight in the important parameters is obtained, the patient-specific model parameters can be identified, and it is possible to adapt the model to the individual patient. Measurements that are an addition to those available in routine clinical care may be included to allow for identification and observation of a greater number of parameters and variables [1]. Examples described in this section are the automatic periodic application of an end-inspiratory and end-expiratory

occlusion manoeuvre, perturbations in the breathing pattern or the use of state-of-the-art noninvasive sensors [50, 58]. Periodically identifying the important parameters could provide better insight in the patient’s physiological state and its development for the clinician.

This also induces the second improvement. The model that is adapted to the patient can predict patient responses to changes in ventilator settings. The ability to predict the response to changing ventilator settings would offer insight in the optimal ventilator settings that current care and equipment cannot provide [53]. This will minimise the risk of VILI and may reduce the duration of mechanical ventilation, which is clinically and economically important [10]. These predictions could be further substantiated through the use of artificial intelligence.

Our new model should focus on the two improvements that are described above. This pleads for a model that has low complexity but is adequately valid, so that all important parameters can be identified with limited information. Another benefit that this induces it that the model will be transparent and understandable for clinicians which may improve the usage. The model parameters should be adaptable to the individual patient to allow for model predictions of patient responses to changing ventilator settings. In the first stadium of development, this model could provide insight in respiratory parameters and variables that the clinician may use to choose the optimal ventilator settings. In a later stadium of development, this model could be the basis of a closed-loop mechanical ventilation system based on the physiology of breathing that can automatically adapt the ventilator settings.

The choice is made to mainly focus our model on the gas exchange and the respiratory drive. We are aware that gaining insight in the respiratory mechanics is, especially in the first stage of mechanical ventilation, of equal or even greater importance. However, the choice to focus on the other aspects of the physiology of breathing is made, because most commercialized systems already focus on the respiratory mechanics. It is suspected that a system that focusses on the gas exchange and the respiratory drive can also be very useful in clinical practice. Especially during

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the later stages of mechanical ventilation when the patient comes near the weaning stage and assessment of the breathing function of the patient becomes of great importance.

It will likely not be possible to provide insight in all the important respiratory parameters and make elaborate predictions with the simple model that is developed in this thesis. However, before the creation of elaborate models, it is important to research what the base structure of these models should be. When the results of simulations with the model are qualitatively similar to the responses measured in an experimental study, we may be able to show the first signs of the use of such a model in clinical practice by identifying aggregated parameter groups and making simple predictions. In the next section, the development of the model is described.

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3. Model development and analysis

In this section, the development and the subsequent dynamical analysis of the model are described. In section 2.4. it was described which requirements for the model followed from current clinical practice. The model should have low complexity and will mainly focus on the gas exchange and the respiratory drive. In section 3.1. the development of a model that meets these requirements is described. Since the model is created on a theoretical basis, it is necessary to find out if the mode has the right structure to accurately describe the real breathing system.

With the dynamical analysis and subsequent simulations described in section 3.2, the dynamic behaviour of the model can be analysed and a hypothesis for the dynamic behaviour of the real breathing system can be stated. This hypothesis will later be tested with an experiment. In section 3.3. the most important results are summarized, interpreted and their implications for the experiment design are stated.

3.1. Model development

3.1.1. The schematic model

In the introduction the workflow of closed loop mechanical ventilation systems was briefly described. The human breathing system is in essence also a closed loop system. In this case, the sensor that measures a physiological variable is not an artificial sensor but are the central and peripheral chemoreceptors that measure the 𝐶𝑂₅ and 𝑂₅ concentrations and the pH of the blood and the extracellular fluid (ECF). In the respiratory control centre (controller) that is located in the brain, the concentrations are compared to the desired value. In this case, the actuation is not a change in ventilator settings but a change in movement of the breathing muscles. The patient (process) may start ventilating more or less to obtain the desired blood gasses.

Figure 2 Schematic overview of the human ventilatory control function.

The development of the model will consist of three main steps:

- Creation of a schematic model

- Derivation of the mathematical equations - Implementation in Simulink

The first step is the creation of a schematic model. In figure 3 this model is presented. The grey blocks in the schematic model represent the four general components of a closed loop system that were described in the previous paragraph: the process, the sensor, the controller and the actuator. The four components have different subsystems that are represented by the white coloured blocks. The arrows represent the information flow or the physiological interactions between the different subsystems. The values of the cursive variables belonging to the arrows are transferred from one subsystem to another. The receiving subsystem will use this

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information to determine the value of other variables. For this, mathematical equations are used that are described in section 3.2.

In the process block there are three subsystems that can store 𝐶𝑂₅ and 𝑂₅: the venous blood, the arterial blood and the alveolar air. In these subsystems, cursive variables are displayed, which represent the state variables. The state variables are variables that are not transported between subsystems but give information about the accumulation of 𝐶𝑂₅ and 𝑂₅ in the storage blocks. In section 3.2. the content of each subsystem is described in detail.

Figure 3 Schematic model of the physiology of breathing

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3.1.2 Mathematical equations describing the relevant physiology

In the former section, an overview of the schematic model with the different subsystems was given. Each subsystem contains mathematical equations that are described in this section. To avoid repetition, only the equations for 𝐶𝑂₅ will be described in this section of the report. In appendix 1 the equations for 𝑂₅ can be found.

Breathing mechanics

Since our model is not mainly focussed on the breathing mechanics, a simple first order system will be used to describe the beathing mechanics. The intrapleural pressure (𝑃_6.(𝑡)) is the pressure in the intrapleural space. Because the lungs and the chest wall pull away from each other on opposite sides of the intrapleural space, the intrapleural pressure is less than barometric pressure (𝑃₇(𝑡)). During inspiration, the inspiratory muscles expand the chest, making 𝑃_6.(𝑡) more negative. The lungs respond by expanding passively.

The alveolar pressure (𝑃₀(𝑡))is equal to the pressure in the alveoli. The transpulmonary pressure (𝑃_1.(𝑡)) is the pressure across the alveolar wall. It is equal to the difference between the alveolar pressure and the intrapleural pressure.

𝑃_1.(𝑡) = 𝑃₀(𝑡) − 𝑃_6.(𝑡) (4)

𝑃_1. is also proportional to the difference between the alveolar volume (V₈(𝑡)) and the Functional residual capacity (𝑉_9:;) and inversely proportional to the respiratory system compliance (𝐶_-*).

𝑃_1.(𝑡) =V₈(𝑡) − 𝑉_9:;

𝐶_-* (5)

Airflow in the airways (𝜙_0<(𝑡)) is proportional to the pressure over the airways (Δ𝑃_0<(𝑡)) and inversely proportional to total respiratory system resistance (𝑅_-*). 𝑃_0<(𝑡) is equal to the difference between 𝑃₀(𝑡) and the ventilator-induced pressure at the mouth (𝑃₌(𝑡)). When the patient is not attached to a ventilator, 𝑃₌(𝑡) equals zero. All pressures have values relative to the atmospheric pressure.

𝜙_0<(𝑡) =𝑃_0<(𝑡)

𝑅_-* =𝑃₀(𝑡) − 𝑃₌(𝑡)

𝑅_-* (6)

Figure 4 The transpulmonary pressure is equal to the difference between the alveolar pressure and the intrapleural pressure.

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In figure 5 a conceptual model of the breathing mechanics can be seen. Using Kirchhoff’s law, it can be determined that the airflow in the airways (𝜙_0<(𝑡)) is equal to the airflow to the alveoli (𝜙₀(𝑡)). This flow is equal to the change in alveolar volume.

𝜙_0<(𝑡) =dV₈(𝑡)

𝑑𝑡 (7)

Kirchhoff’s law also states that the sum of all the pressures in the conceptual model should be equal to zero.

𝑃₌(𝑡) − 𝑃_0<(𝑡) − 𝑃_1.(𝑡) − 𝑃_6.(𝑡) = 0 (8)

After combining the formed equations, equation 9 is obtained.

𝑅_-*⋅ 𝐶_-*⋅dV₈(𝑡)

𝑑𝑡 + (V₈(𝑡) − 𝑉_9:;) = 𝐶_-*⋅ (𝑃₌(𝑡) − 𝑃_6.(𝑡)) (9)

Explanation: From this equation, the alveolar volume and airflow as a function of time can be determined when the pressures and resistance and compliance are known. The values of the alveolar volume and airflow will be transported to the subsystem ‘the alveolar air’ (figure 3). The system ‘the alveolar air’ will use its own equations to determine the value of other variables. These variables are in turn transported to other blocks. This is the global workflow of a mathematical model.

Alveolar air

The change in the number of 𝐶𝑂₅ molecules in the alveolar air (𝑚_0 ;?_!(𝑡)) depends on the diffusion flow from the capillaries to the alveolar space (𝜙_@4A ;?_!(𝑡)) and the outflow of 𝐶𝑂₅ from the body (𝜙_0< ;?_!(𝑡)).

𝑑𝑚_0 ;?_!(𝑡)

𝑑𝑡 = 𝜙_@4A ;?_!(𝑡) − 𝜙_0< ;?_!(𝑡) (10)

The relation between the partial pressure of 𝐶𝑂₅ in the alveolar air (𝑃_0 ;?_!) and the

concentration of 𝐶𝑂₅ in the alveolar air is linear. The factor 𝑘_B describes the linear relation between both variables.

Figure 5 schematic overview of the respiratory mechanics.

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𝑃_0 ;?_!(𝑡) = 𝑘_B⋅𝑚_0 ;?_!(𝑡)

𝑉₀(𝑡) (11)

The flow of 𝐶𝑂₅ in and out of the lungs (𝜙_0< ;?_!(𝑡)) is dependent on the airflow (𝜙_0<(𝑡)) and during exhalation on the concentration of 𝐶𝑂₅ in the lungs (𝐶₀_"#!(𝑡)) or during inhalation on the concentration of 𝐶𝑂₅ in the inspired air (𝐶_#!(_"#!(𝑡)).

Inhalation

𝜙_0< ;?_!(𝑡) = 𝐶_#!(

"#!(𝑡) ⋅ 𝜙_0<(𝑡) (12)

Exhalation

𝜙_0< ;?_!(𝑡) = 𝐶₀_"#!(𝑡) ⋅ 𝜙_0<(𝑡) (13)

Diffusion between alveolar air and the pulmonary capillaries

The movement of 𝐶𝑂₅ across the alveolar blood-gas barrier occurs by simple diffusion. Fick’s law describes that the net flow is proportional to the difference in partial pressures of 𝐶𝑂₅ in the alveolar air and the blood. The diffusion coefficient (𝐷_/_"#!) is dependent on the properties of both the barrier and the gas. If we assume that the alveolar air, blood-gas barrier and pulmonary capillary blood are uniform in space and time, then the net diffusion of 𝐶𝑂₅ from the alveolar air to pulmonary capillary blood is described by equation 14.

𝜙_@4A ;?_!(𝑡) = 𝐷_/

"#!F𝑃_%;?

!(𝑡) − 𝑃₀

"#!(𝑡)G (14)

Arterial blood

The change of the total 𝐶𝑂₅ mass in the arterial blood (𝑚_#_$%!(𝑡)) is equal to the sum of the flows that carry 𝐶𝑂₅ in and out of the compartment. The outgoing flow consists of the diffusion flow and the flow of 𝐶𝑂₅ molecules from the arterial blood to the venous blood (𝜙_#%_"#!(𝑡)). The ingoing flow is the flow of 𝐶𝑂₅ molecules from the venous blood to the arterial blood (𝜙_%#_"#!(𝑡))

𝑑𝑚_#

$%!(𝑡)

𝑑𝑡 = 𝜙_%#_"#!(𝑡) − 𝜙_@4A_"#!(𝑡) − 𝜙_#%_"#!(𝑡)

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The flow of 𝐶𝑂₅ from the venous to the arterial compartment (𝜙_%#_"#!(𝑡)) and the flow of 𝐶𝑂₅ from the arterial to the venous compartment (𝜙_#%_"#!(𝑡)) are described by equation 16 and 17.

The flows between the blood compartment are equal to the product of the blood flow in the compartment (𝑄(𝑡)) and the concentration of 𝐶𝑂₅ in the sending compartment.

𝜙_%#_"#!(𝑡) = 𝑄(𝑡) ⋅𝑚_%_"#!(𝑡)

𝑉_% (16)

𝜙_#%_"#!(𝑡) = 𝑄(𝑡) ⋅𝑚_#

"#!(𝑡) 𝑉_#

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Dynamic modelling of the physiology of breathing to improve mechanical ventilation

Dynamic modelling of the physiology of breathing to improve mechanical ventilation

Dynamic modelling of the physiology of breathing to improve mechanical ventilation

Summary

Table of contents

Glossary

1. Introduction

2. State-of-the-art of closed-loop mechanical ventilation and possible improvements.

3. Model development and analysis